×

zbMATH — the first resource for mathematics

Completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability. (English) Zbl 0181.54703

Keywords:
fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability. London: Oxford Univ. Press 1961.
[2] Eckhaus, W., Studies in Nonlinear Stability Theory. Berlin-Heidelberg-New York: Springer 1965. · Zbl 0125.33101
[3] Di Prima, R. C., Vector Eigenfunction Expansions for the Growth of Taylor Vortices in the Flow between Rotating Cylinders, Nonlinear Partial Differential Equations. New York: Academic Press 1967, pages 19-42. · Zbl 0173.53301
[4] Schensted, I. V., Contributions to the Theory of Hydrodynamic Stability. Ph. D. Thesis. U. of Michigan, Ann Arbor (1960).
[5] Yudovich, V. I. (Iudovich), Stability of steady flows of viscous incompressible fluids. Soviet Physics-Doklady 10, 293-295 (1965). · Zbl 0139.21901
[6] Naimark, M. A., On some criteria of completeness of the system of eigen and associated vectors of a linear operator in Hilbert space. Doklady Akad. Nauk. SSSR 98, 727-730 (1954).
[7] Mikhlin, S. G., The Problem of the Minimum of a Quadratic Functional. San Francisco: Holden-Day 1965. · Zbl 0121.32801
[8] Kato, T., Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0148.12601
[9] Agmon, S., Lectures on Elliptic Boundary Value Problems. New York: Van Nostrand 1965. · Zbl 0142.37401
[10] Di Prima, R. C., & Coda, H. T. Pan, The stability of flow between concentric cylindrical surfaces with a circular magnetic field. Journal of Applied Mathematics and Physics (ZAMP) 15, 560-567 (1964). · Zbl 0133.44701
[11] Davis, S. H., On the principle of exchange of stabilities. To appear, Proceedings of the Royal Society of London. · Zbl 0181.55603
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.